The Human Rights Law Centre, the Council for International Development and the Australian Council of Social Service sent legal advice about detained child and youth refugees being abused to the commission more than 12 months ago.

The call has the support of Australia's Human Rights Commission president Gillian Triggs who agrees the commission's investigative charter should be extended following revelations this week of ongoing violence at the Nauru facility.

Leaked files from the facility show the Federal Government failed to take action even though it knew asylum seeker children and adults were being abused.

The paper trail reveals there were more than 2000 reported incidents of physical and sexual assault and self-harm between 2013 and 2015.

Human Rights Law Centre executive director Hugh de Kretser said commissioner Justice Peter McClellan had the power to investigate the claims.

"In a nutshell, the advice says that while the royal commission can't obviously go to Nauru and exercise coercive powers on Nauru, it can look at the response of the Australian Government and its contractors to child sexual abuse that occurred on Australia's detention centre on Nauru," he told the ABC.

"We've taken the step to make this advice public on the back of the widespread evidence of ongoing harm to innocent people, including children, that was revealed this week through the leaked files."

Council for International Development executive director Marc Purcell said the Commonwealth was responsible for "harm being caused to people on Nauru."

Ms Triggs rejected Immigration Minister Peter Dutton's statement that "Nauru is not part of Australia so this is an issue for the Nauruan Government."

"I think that a royal commission could investigate, in my view, matters for which Australia … have managed and paid for the entire process," Ms Triggs told Radio National. - ARM NEWSDESK